I am having trouble drawing integrals onto the spectrum that I have drawn in to Originlabs. Ideally I would like to draw integrals something like this (along with the integration values);
You can use Integrate gadget to output partial integral curve data to worksheet easily and then add them to the graph (maybe you will need a Right-Y layer for those integral curves).
Origin supports selecting subranges in graph and do analysis.
So after plotting the spectrum, use Selection button (7th button on Tools toolbar) to select the different regions of the plot where you want to calculate integral.
Then choose Analaysis: Mathematics: Integration. In the dialog, set Plot Integral Curve to be Source Graph. Click OK --> Integral plot will draw in each subrange.